Let ##(2x+3) ^3## be a given binomial.

From the binomial expression write down the general term. Let this term be the r+1 th term. Now simplify this general term. If this general term is a constant term then it should not contain the variable x.

Let us write the general term of the above binomial.

##T_(r+1)## = ## ^3 C_r## ##(2x)^(3-r)## ##3^r##

simplifying we get ##T_(r+1)##= ## ^3 C_r## ##2^(3-r)## ##3^r## ##x^(3-r)##

Now for this term to be the constant term ##x^(3-r)## should be equal to 1.

Therefore ##x^(3-r)##= ##x^0##

=> 3-r =0

=> r=3

Thus the fourth term in the expansion is the constant term. By putting r=3 in the general term we will get the value of the constant term.